Combinatorics

Hypergeometric function of a matrix argument

Hypergeometric distribution

Laurent series

Hypergeometric function

Pure mathematics

Mathematics

Mathematical physics

Biology

Basic hypergeometric series

Algebra over a field

Generalized hypergeometric function

Series (stratigraphy)

Polytope

Paleontology

Artificial intelligence

Regularization (linguistics)

Computer science

Feynman diagram

Feynman integral

Journal of High Energy Physics

We show that almost all Feynman integrals as well as their coefficients in a Laurent series in dimensional regularization can be written in terms of Horn hypergeometric functions. By applying the results of Gelfand-Kapranov-Zelevinsky (GKZ) we derive a formula for a class of hypergeometric series representations of Feynman integrals, which can be obtained by triangulations of the Newton polytope ∆G corresponding to the Lee- Pomeransky polynomial G. Those series can be of higher dimension, but converge fast for convenient kinematics, which also allows numerical applications. Further, we discuss possible difficulties which can arise in a practical usage of this approach and give strategies to solve them.

Hypergeometric series representations of Feynman integrals by GKZ hypergeometric systems